Durango Bill's
Lowball (Low Ball) Poker Probabilities
8 Card, 9 Card,
and 10 Card Lowball (Low Ball) Poker Probabilities
for various wild card specifications
for various wild card specifications
The tables below show the probabilities of being dealt various lowball Poker hands with different wild card specifications. Each Poker hand consists of selecting the 5 best cards from a random 8 card deal.
The introduction of wild cards greatly complicates the calculations. Thus, to produce the results shown here, the author wrote a computer program that would generate all possible Poker hands. Each of these Poker hands was evaluated for the lowest high card (or worse - if pairs exist). Wild cards are automatically assigned the lowest ranks that do not match any other rank.
Data from this page may be freely used provided it includes an acknowledgement to the author.
8 card lowball Poker probabilities if there are no wild cards
(Computer program and data by Bill Butler)
Lowball Hand Nbr of Hands Probability
-----------------------------------------------
Five high 9,856,000 0.01309701
Six high 35,563,520 0.04725810
Seven high 74,019,840 0.09836025
Eight high 113,971,200 0.15144907
Nine high 140,851,200 0.18716819
Ten high 143,216,640 0.19031147
Jack high 118,487,040 0.15744988
Queen high 75,694,080 0.10058504
King high 32,947,200 0.04378143
Pair or worse 7,931,430 0.01053957
Total 752,538,150 1.00000000
= COMBIN(52,8)
8 card lowball Poker probabilities if one ordinary Joker is added to the deck
In lowball Poker, a Joker/wild card can be used to fill in any unused rank.
(Computer program and data by Bill Butler)
Lowball Hand Nbr of Hands Probability
-----------------------------------------------
Five high 21,554,304 0.02431880
Six high 51,093,760 0.05764690
Seven high 95,178,240 0.10738554
Eight high 137,827,200 0.15550453
Nine high 163,681,280 0.18467459
Ten high 161,677,824 0.18241417
Jack high 130,667,520 0.14742657
Queen high 81,713,280 0.09219360
King high 34,777,600 0.03923808
Pair or worse 8,151,702 0.00919722
Total 886,322,710 1.00000000
= COMBIN(53,8)
8 card lowball Poker probabilities if two Jokers are added to the deck
In lowball Poker, a Joker/wild card can be used to fill in any unused rank.
(Computer program and data by Bill Butler)
Lowball Hand Nbr of Hands Probability
-----------------------------------------------
Five high 39,007,056 0.03748999
Six high 69,992,400 0.06727026
Seven high 119,709,240 0.11505351
Eight high 164,644,200 0.15824086
Nine high 188,785,632 0.18144338
Ten high 181,629,984 0.17456603
Jack high 143,634,600 0.13804836
Queen high 88,025,080 0.08460161
King high 36,663,440 0.03523753
Pair or worse 8,374,158 0.00804847
Total 1,040,465,790 1.00000000
= COMBIN(54,8)
8 card lowball Poker probabilities with One-eyed Jacks wild
In lowball Poker, a Joker/wild card can be used to fill in any unused rank.
(Computer program and data by Bill Butler)
Lowball Hand Nbr of Hands Probability
-----------------------------------------------
Five high 33,214,800 0.04413703
Six high 58,348,240 0.07753526
Seven high 97,489,080 0.12954703
Eight high 130,018,280 0.17277301
Nine high 142,971,360 0.18998553
Ten high 129,591,840 0.17220634
Jack high 57,477,540 0.07637824
Queen high 68,547,120 0.09108790
King high 28,496,820 0.03786761
Pair or worse 6,383,070 0.00848206
Total 752,538,150 1.00000000
= COMBIN(52,8)
8 card lowball Poker probabilities with Deuces (2’s) wild
If deuces are wild, then holding a single deuce in your hand is not much different than lowball Poker with nothing wild. However, if you have two or more deuces, then one of them can fill in the natural omission of a “2” while the others can fill in other blank ranks.
(Computer program and data by Bill Butler)
Lowball Hand Nbr of Hands Probability
-----------------------------------------------
Five high 24,755,612 0.03289616
Six high 45,263,133 0.06014729
Seven high 81,436,729 0.10821608
Eight high 116,759,205 0.15515387
Nine high 138,182,241 0.18362158
Ten high 135,995,757 0.18071610
Jack high 109,075,913 0.14494403
Queen high 67,143,029 0.08922209
King high 27,735,665 0.03685616
Pair or worse 6,190,866 0.00822665
Total 752,538,150 1.00000000
= COMBIN(52,8)
8 card lowball Poker probabilities with 2 Jokers,
One-eyed Jacks, and Deuces (2’s) wild
(8 out of 54 cards are wild)
(Computer program and data by Bill Butler)
Lowball Hand Nbr of Hands Probability
-----------------------------------------------
Five high 113,417,757 0.10900671
Six high 107,864,298 0.10366924
Seven high 149,937,010 0.14410566
Eight high 177,112,730 0.17022446
Nine high 178,028,130 0.17110426
Ten high 149,636,298 0.14381664
Jack high 62,413,400 0.05998602
Queen high 70,405,598 0.06766738
King high 26,469,206 0.02543977
Pair or worse 5,181,363 0.00497985
Total 1,040,465,790 1.00000000
= COMBIN(54,8)
9 Card Lowball
Poker Probabilities
The tables below show the probabilities of being dealt various lowball Poker hands with different wild card specifications. Each Poker hand consists of the best 5 cards from a 9 card deal.
The introduction of wild cards greatly complicates the calculations. Thus, to produce the results shown here, the author wrote a computer program that would generate all possible Poker hands. Each of these Poker hands was evaluated for the lowest high card (or worse - if pairs exist). Wild cards are automatically assigned the lowest ranks that do not match any other rank.
Data from this page may be freely used provided it includes an acknowledgement to the author.
9 card lowball Poker probabilities if there are no wild cards
(Computer program and data by Bill Butler)
Lowball Hand Nbr of Hands Probability
-----------------------------------------------
Five high 91,126,080 0.02476874
Six high 293,736,000 0.07983962
Seven high 538,618,560 0.14640052
Eight high 717,886,400 0.19512685
Nine high 750,512,000 0.20399473
Ten high 625,806,720 0.17009891
Jack high 406,492,800 0.11048776
Queen high 191,368,320 0.05201533
King high 55,915,200 0.01519817
Pair or worse 7,613,320 0.00206936
Total 3,679,075,400 1.00000000
= COMBIN(52,9)
9 card lowball Poker probabilities if one ordinary Joker is added to the deck
In lowball Poker, a Joker/wild card can be used to fill in any unused rank.
(Computer program and data by Bill Butler)
Lowball Hand Nbr of Hands Probability
-----------------------------------------------
Five high 197,599,760 0.04458867
Six high 415,844,320 0.09383587
Seven high 684,142,080 0.15437765
Eight high 858,581,360 0.19374012
Nine high 862,942,976 0.19472433
Ten high 698,975,424 0.15772481
Jack high 443,312,640 0.10003414
Queen high 204,148,560 0.04606642
King high 58,312,320 0.01315826
Pair or worse 7,754,110 0.00174973
Total 4,431,613,550 1.00000000
= COMBIN(53,9)
9 card lowball Poker probabilities if two Jokers are added to the deck
In lowball Poker, a Joker/wild card can be used to fill in any unused rank.
(Computer program and data by Bill Butler)
Lowball Hand Nbr of Hands Probability
-----------------------------------------------
Five high 356,442,464 0.06702646
Six high 563,093,120 0.10588565
Seven high 851,507,520 0.16011992
Eight high 1,015,541,408 0.19096532
Nine high 985,645,696 0.18534365
Ten high 777,438,720 0.14619181
Jack high 482,183,040 0.09067108
Queen high 217,428,640 0.04088591
King high 60,760,128 0.01142551
Pair or worse 7,895,524 0.00148470
Total 5,317,936,260 1.00000000
= COMBIN(54,9)
9 card lowball Poker probabilities with One-eyed Jacks wild
In lowball Poker, a Joker/wild card can be used to fill in any unused rank.
(Computer program and data by Bill Butler)
Lowball Hand Nbr of Hands Probability
-----------------------------------------------
Five high 287,194,720 0.07806166
Six high 440,752,000 0.11979966
Seven high 645,801,920 0.17553376
Eight high 738,879,008 0.20083280
Nine high 677,869,696 0.18425001
Ten high 493,725,696 0.13419831
Jack high 176,937,840 0.04809302
Queen high 165,884,080 0.04508852
King high 46,145,792 0.01254277
Pair or worse 5,884,648 0.00159949
Total 3,679,075,400 1.00000000
= COMBIN(52,9)
9 card lowball Poker probabilities with Deuces (2’s) wild
If deuces are wild, then holding a single deuce in your hand is not much different than lowball Poker with nothing wild. However, if you have two or more deuces, then one of them can fill in the natural omission of a “2” while the others can fill in other blank ranks.
(Computer program and data by Bill Butler)
Lowball Hand Nbr of Hands Probability
-----------------------------------------------
Five high 218,310,256 0.05933835
Six high 352,923,704 0.09592728
Seven high 563,756,176 0.15323311
Eight high 702,499,992 0.19094471
Nine high 704,389,776 0.19145837
Ten high 568,255,992 0.15445620
Jack high 357,057,424 0.09705086
Queen high 161,447,256 0.04388256
King high 44,722,832 0.01215600
Pair or worse 5,711,992 0.00155256
Total 3,679,075,400 1.00000000
= COMBIN(52,9)
9 card lowball Poker probabilities with 2 Jokers,
One-eyed Jacks, and Deuces (2’s) wild
(8 out of 54 cards are wild)
(Computer program and data by Bill Butler)
Lowball Hand Nbr of Hands Probability
-----------------------------------------------
Five high 954,790,558 0.17954156
Six high 766,999,812 0.14422885
Seven high 936,352,900 0.17607449
Eight high 948,976,548 0.17844827
Nine high 794,490,340 0.14939824
Ten high 534,576,644 0.10052333
Jack high 179,408,656 0.03373652
Queen high 158,183,176 0.02974522
King high 39,665,336 0.00745878
Pair or worse 4,492,290 0.00084474
Total 5,317,936,260 1.00000000
= COMBIN(54,9)
10 Card Lowball
Poker Probabilities
Just in case anyone is interested in what kind of a 5-card lowball Poker hand you can get out of a total deal of 10 cards, the computer program can also tabulate these results.
Data from this page may be freely used provided it includes an acknowledgement to the author.
10 card lowball Poker probabilities if there are no wild cards
(Computer program and data by Bill Butler)
Lowball Hand Nbr of Hands Probability
-----------------------------------------------
Five high 658,829,280 0.04164528
Six high 1,893,034,080 0.11966063
Seven high 3,050,318,880 0.19281379
Eight high 3,508,367,520 0.22176752
Nine high 3,091,197,760 0.19539779
Ten high 2,104,409,664 0.13302190
Jack high 1,067,774,400 0.06749512
Queen high 368,575,680 0.02329805
King high 71,961,120 0.00454874
Pair or worse 5,555,836 0.00035119
Total 15,820,024,220 1.00000000
= COMBIN(54,10)
Also please see 5 card lowball Poker probabilities
Also please see 6 card lowball Poker probabilities
Also please see 7 card lowball Poker probabilities
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